Edge Modes Waves in Superlattices in Quantum Hall Effect Regime

The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along the boundary. The constitutive relations expressing the edge charge and current densities in terms of the fields at the boundary are derived. One of them is similar to the London equation for superconductor currents. The dispersion relation and wave polarizations for the momenta region $w/c<k$ are also obtained for propagation along the borderlines of the electron gases. It follows that the modes have no dispersion at any frequency. The static limit solutions complete the definition at the boundary of the formerly determined interior field configurations showing a Meissner like effect. The results underline that various of the current theoretical approaches to edge excitations could be appropriate for superlattice structures but can fail to describe standard planar samples.